Quadratic-Linear Algebra
From Handwiki  | This article relies largely or entirely on a single source. (April 2024) |
In mathematics, a quadratic-linear algebra is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators. They were introduced by Polishchuk and Positselski (2005, p.101). An example is the universal enveloping algebra of a Lie algebra, with generators a basis of the Lie algebra and relations of the form XY – YX – [X, Y] = 0.
References
- Polishchuk, Alexander; Positselski, Leonid (2005), Quadratic algebras, University Lecture Series, 37, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3834-1, https://books.google.com/books?id=5_ZrCKU4NpAC
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Categories: [Abstract algebra]
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